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Interference patterns like those produced by a two-slit experiment make sense to me when I imagine light as a wave, with peaks cancelling out troughs in some locations and two peaks adding together in other locations. What doesn't make sense to me is how the particle nature of light is explained in this instance. How does a phase shift result in a lack of photons striking some spots and more photons striking others?

dibutin
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    Are you asking how one can use the double slit experiment to show the particle nature of light? Or are you asking how we move from the "wave picture" to the "photon picture"? – BioPhysicist Feb 27 '20 at 04:20
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    Your seem to be a victim of a common misconception that the waves are a collective behavior of many particles somehow interfering or interacting with each other. This is incorrect. Each photon is a wave on its own that interferes only with itself. Each photon passes through both slits at the same time. Two photons neither interfere as waves nor interact as particles with each other. Photons are very lonely creatures, they are completely unaware of each other's existence. – safesphere Feb 27 '20 at 05:00
  • @YuvrajSingh... I can't tell what you are trying to say in your comment – BioPhysicist Feb 27 '20 at 12:22
  • @AaronStevens what I mean was, that is there exist theory which add some points which Youngs missed. – आर्यभट्ट Feb 27 '20 at 14:09
  • Photons aren’t particles (as we understand them from our macroscopic experience), so you shouldn’t be surprised when they don’t act like particles. They also aren’t waves, so you shouldn’t be surprised when they don’t act like waves. They are quantum fields, and so you should always expect them to act like quantum fields. – Mike Scott Feb 27 '20 at 15:57

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The particle nature of light comes up when you are detecting the photon. It always appears localised at some point. This can be seen in double slit experiments done by sending one photon at a time. This has been done but I wasn’t able to find images (thank you @annav). So here is the image of the experiment done which shows the accumulation of detections over time.

enter image description here

So now that we know photons come in discrete chunks (as they are localised on our detectors) why are there regions on the detector where no photons go? Well that is because the probability (amplitude) distribution of the photon has wavelike properties. This is what quantum mechanics tells us. This means that each photon interferes with itself.

Superfast Jellyfish
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    see this for photons/light http://www.sps.ch/en/articles/progresses/wave_particle_duality_of_light_for_the_classroom_13/ – anna v Feb 27 '20 at 09:13
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    This means that each photon interferes with itself. Or it just means that the probability amplitude looks just like an interference pattern. Does this actually prove that there is an actual mechanism of self-interference? – BioPhysicist Feb 27 '20 at 12:18
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    @AaronStevens It appears as if each individual photon followed the same rules as a wave of photons coming through the slits. It doesn't prove that's what actually happens, of course. All it requires is that photons behave like quanta - waves with the minimal possible amplitude. And of course, there's plenty of arguments about all the tiny details of the experimental setup, like "the barrier is actually also a sea of non-factorizable quanta, which interact with the photon as it goes through the slits, not just a magical "photon's can't go here" areas". – Luaan Feb 27 '20 at 13:50
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    Don't assume the photon, as a particle, must choose which slit to go through. Until it hits the film, it's Schrodinger's photon, and may go partly through one slit and partly through another. – Cristobol Polychronopolis Feb 27 '20 at 15:08
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They don't. Interference patterns are a product of waves, not (classical) particles. The particle nature of light is not explained by interference patterns.

Young's slits and the resulting interference pattern are not evidence of the corpuscular theory, as once the particle theory was called. Interference patterns were taken as direct evidence that light is a wave not a particle.

That we now understand something about photons exhibiting wave-particle duality does not mean that any particular/specific result of an experiment that supports one interpretation of wave-particle duality has to support the other.

How does a phase shift result in a lack of photons striking some spots and more photons striking others?

It tells the obsever that photons exhibit wave characterstics, that they are in some way waves that interfere with themselves.

Smartybartfast
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    "The particle nature of light is not explained by interference patterns." the inverse though does : "the probability distribution of photons in a double slit experiment shows interference patterns that are the same as the light built up wit the hν of those photons" http://www.sps.ch/en/articles/progresses/wave_particle_duality_of_light_for_the_classroom_13/ – anna v Feb 27 '20 at 09:16